Problem: Simplify the following expression and state the condition under which the simplification is valid. $k = \dfrac{-4p^2 - 20p - 16}{-7p^2 + 35p + 252}$
First factor out the greatest common factors in the numerator and in the denominator. $ k = \dfrac {-4(p^2 + 5p + 4)} {-7(p^2 - 5p - 36)} $ $ k = \dfrac{4}{7} \cdot \dfrac{p^2 + 5p + 4}{p^2 - 5p - 36} $ Next factor the numerator and denominator. $ k = \dfrac{4}{7} \cdot \dfrac{(p + 4)(p + 1)}{(p + 4)(p - 9)}$ Assuming $p \neq -4$ , we can cancel the $p + 4$ $ k = \dfrac{4}{7} \cdot \dfrac{p + 1}{p - 9}$ Therefore: $ k = \dfrac{ 4(p + 1)}{ 7(p - 9)}$, $p \neq -4$